Properties

Modulus 83
Structure \(C_{82}\)
Order 82

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(83)
 
pari: g = idealstar(,83,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 82
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{82}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{83}(2,\cdot)$

First 32 of 82 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
\(\chi_{83}(1,\cdot)\) 83.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{83}(2,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{1}{82}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{27}{82}\right)\) \(e\left(\frac{73}{82}\right)\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{3}{82}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{12}{41}\right)\)
\(\chi_{83}(3,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{24}{41}\right)\) \(e\left(\frac{3}{41}\right)\)
\(\chi_{83}(4,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{24}{41}\right)\)
\(\chi_{83}(5,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{27}{82}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{73}{82}\right)\) \(e\left(\frac{3}{82}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{81}{82}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{37}{41}\right)\)
\(\chi_{83}(6,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{73}{82}\right)\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{3}{82}\right)\) \(e\left(\frac{81}{82}\right)\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{55}{82}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{15}{41}\right)\)
\(\chi_{83}(7,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{30}{41}\right)\) \(e\left(\frac{14}{41}\right)\)
\(\chi_{83}(8,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{3}{82}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{81}{82}\right)\) \(e\left(\frac{55}{82}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{9}{82}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{36}{41}\right)\)
\(\chi_{83}(9,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{7}{41}\right)\) \(e\left(\frac{6}{41}\right)\)
\(\chi_{83}(10,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{24}{41}\right)\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{30}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{7}{41}\right)\) \(e\left(\frac{23}{41}\right)\) \(e\left(\frac{8}{41}\right)\)
\(\chi_{83}(11,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{24}{41}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{1}{41}\right)\)
\(\chi_{83}(12,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{33}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{39}{41}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{27}{41}\right)\)
\(\chi_{83}(13,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{77}{82}\right)\) \(e\left(\frac{25}{41}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{29}{82}\right)\) \(e\left(\frac{45}{82}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{67}{82}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{22}{41}\right)\)
\(\chi_{83}(14,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{9}{82}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{79}{82}\right)\) \(e\left(\frac{1}{82}\right)\) \(e\left(\frac{36}{41}\right)\) \(e\left(\frac{27}{82}\right)\) \(e\left(\frac{33}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{26}{41}\right)\)
\(\chi_{83}(15,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{17}{82}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{49}{82}\right)\) \(e\left(\frac{11}{82}\right)\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{51}{82}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{33}{41}\right)\) \(e\left(\frac{40}{41}\right)\)
\(\chi_{83}(16,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{23}{41}\right)\) \(e\left(\frac{16}{41}\right)\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{7}{41}\right)\)
\(\chi_{83}(17,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{7}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{19}{41}\right)\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{16}{41}\right)\)
\(\chi_{83}(18,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{63}{82}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{22}{41}\right)\) \(e\left(\frac{61}{82}\right)\) \(e\left(\frac{7}{82}\right)\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{25}{82}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{18}{41}\right)\)
\(\chi_{83}(19,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{47}{82}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{39}{82}\right)\) \(e\left(\frac{69}{82}\right)\) \(e\left(\frac{24}{41}\right)\) \(e\left(\frac{59}{82}\right)\) \(e\left(\frac{22}{41}\right)\) \(e\left(\frac{2}{41}\right)\) \(e\left(\frac{31}{41}\right)\)
\(\chi_{83}(20,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{29}{82}\right)\) \(e\left(\frac{19}{41}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{45}{82}\right)\) \(e\left(\frac{67}{82}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{5}{82}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{20}{41}\right)\)
\(\chi_{83}(21,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{10}{41}\right)\) \(e\left(\frac{39}{41}\right)\) \(e\left(\frac{14}{41}\right)\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{33}{41}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{20}{41}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{17}{41}\right)\)
\(\chi_{83}(22,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{25}{82}\right)\) \(e\left(\frac{39}{41}\right)\) \(e\left(\frac{25}{41}\right)\) \(e\left(\frac{19}{82}\right)\) \(e\left(\frac{21}{82}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{75}{82}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{22}{41}\right)\) \(e\left(\frac{13}{41}\right)\)
\(\chi_{83}(23,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{30}{41}\right)\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{19}{41}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{8}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{20}{41}\right)\) \(e\left(\frac{23}{41}\right)\)
\(\chi_{83}(24,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{75}{82}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{57}{82}\right)\) \(e\left(\frac{63}{82}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{61}{82}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{25}{41}\right)\) \(e\left(\frac{39}{41}\right)\)
\(\chi_{83}(25,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{33}{41}\right)\)
\(\chi_{83}(26,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{39}{41}\right)\) \(e\left(\frac{20}{41}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{25}{41}\right)\) \(e\left(\frac{35}{41}\right)\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{34}{41}\right)\)
\(\chi_{83}(27,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{26}{41}\right)\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{11}{41}\right)\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{13}{41}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{9}{41}\right)\)
\(\chi_{83}(28,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{10}{41}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{37}{41}\right)\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{23}{41}\right)\) \(e\left(\frac{17}{41}\right)\) \(e\left(\frac{38}{41}\right)\)
\(\chi_{83}(29,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{22}{41}\right)\) \(e\left(\frac{12}{41}\right)\) \(e\left(\frac{39}{41}\right)\) \(e\left(\frac{28}{41}\right)\) \(e\left(\frac{7}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{3}{41}\right)\) \(e\left(\frac{4}{41}\right)\) \(e\left(\frac{21}{41}\right)\)
\(\chi_{83}(30,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{9}{41}\right)\) \(e\left(\frac{33}{41}\right)\) \(e\left(\frac{18}{41}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{1}{41}\right)\) \(e\left(\frac{31}{41}\right)\) \(e\left(\frac{27}{41}\right)\) \(e\left(\frac{25}{41}\right)\) \(e\left(\frac{6}{41}\right)\) \(e\left(\frac{11}{41}\right)\)
\(\chi_{83}(31,\cdot)\) 83.c 41 Yes \(1\) \(1\) \(e\left(\frac{19}{41}\right)\) \(e\left(\frac{15}{41}\right)\) \(e\left(\frac{38}{41}\right)\) \(e\left(\frac{21}{41}\right)\) \(e\left(\frac{34}{41}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{16}{41}\right)\) \(e\left(\frac{30}{41}\right)\) \(e\left(\frac{40}{41}\right)\) \(e\left(\frac{5}{41}\right)\)
\(\chi_{83}(32,\cdot)\) 83.d 82 Yes \(-1\) \(1\) \(e\left(\frac{5}{82}\right)\) \(e\left(\frac{16}{41}\right)\) \(e\left(\frac{5}{41}\right)\) \(e\left(\frac{53}{82}\right)\) \(e\left(\frac{37}{82}\right)\) \(e\left(\frac{20}{41}\right)\) \(e\left(\frac{15}{82}\right)\) \(e\left(\frac{32}{41}\right)\) \(e\left(\frac{29}{41}\right)\) \(e\left(\frac{19}{41}\right)\)